Hall Ticket No Question Paper Code: AIT002
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
B.Tech IV Semester End Examinations ( Supplementary) - July, 2018 Regulation: IARE – R16
THEORY OF COMPUTATION
Time: 3 Hours (Common to CSE | IT) Max Marks: 70
Answer ONE Question from each Unit All Questions Carry Equal Marks
All parts of the question must be answered in one place only
UNIT – I
1. (a) Define the following terms and give an example for each: i) Language ii) Star closure of a language
iii) Non Deterministic Finite Automata (NFA) [7M]
(b) Define a Deterministic finite automata (DFA). Design a DFA for the language over {1,0} con- sisting of strings ending with 10.
[7M]
2. (a) Design NFA for recognizing relational operators of C Programming language. [7M]
(b) Convert the following NFA to DFA. [7M]
Figure 1
UNIT – II
3. (a) Construct the NFA for the regular expression (a + b)(a∗+b∗). [7M]
(b) Give regular expression for the following language L over {1,0} where L consists of strings of
length multiples of 3. [7M]
4. (a) Describe the closure properties of Regular Languages. [7M]
(b) Write the right linear grammar for the regular expression (0+1)*. [7M]
UNIT – III
5. (a) Give the context free grammar for the following language: L= {anbm / n=m+2 }. [7M]
(b) Convert the following grammar into CNF: [7M]
S –> aAa | bBb |ε A –> C | a
B –> C | b C –> CDE | ε D –> A | B | ab
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6. (a) State and explain with an example pumping lemma theorem for context free languages. [7M]
(b) Consider the Grammar G=(V,T,E,P) with the following productions.
E –> E + T | F, T –> T * F | F, F –> ( E ) | id
Write the leftmost and rightmost derivation and parse tree for the string id+id*id. Is the grammar
ambiguous? [7M]
UNIT – IV
7. (a) Compare DPDA and NPDA. Give one example for each. [7M]
(b) Convert the following grammar to a PDA [7M]
I –> a | b | Ia | Ib | I0 | I1 E –> I | E * E | E + E | (E)
8. (a) Design a NPDA to accept a balanced strings of parentheses. [7M]
(b) Explain the following [7M]
i. PDA accepting through empty stack ii. PDA Accepting through final state.
UNIT – V
9. (a) Define a Turing machine and with a neat diagram, explain its working principle. [7M]
(b) Design a Turing machine that will accept the language L over {a, b}whereL={anbncn}.|n≥0.
[7M]
10. (a) List the different types of languages and show the relationship using chomsky hierarchy. [7M]
(b) Define the following with an example: [7M]
i. Recursively enumerable languages ii. Recursive languages
iii. Universal languages
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